Related papers: JAX Autodiff from a Linear Logic Perspective (Exte…

Autoformalization is the process of automatically translating from natural language mathematics to formal specifications and proofs. A successful autoformalization system could advance the fields of formal verification, program synthesis,…

We show how to apply forward and reverse mode Combinatory Homomorphic Automatic Differentiation (CHAD) to total functional programming languages with expressive type systems featuring the combination of - tuple types; - sum types; -…

The recently introduced dependent typed higher-order logic (DHOL) offers an interesting compromise between expressiveness and automation support. It sacrifices the decidability of its type system in order to significantly extend its…

We derive algorithms for higher order derivative computation of the rectangular $QR$ and eigenvalue decomposition of symmetric matrices with distinct eigenvalues in the forward and reverse mode of algorithmic differentiation (AD) using…

Dependent type theory gives an expressive type system facilitating succinct formalizations of mathematical concepts. In practice, it is mainly used for interactive theorem proving with intensional type theories, with PVS being a notable…

This paper concerns the explicit treatment of substitutions in the lambda calculus. One of its contributions is the simplification and rationalization of the suspension calculus that embodies such a treatment. The earlier version of this…

We present the guarded lambda-calculus, an extension of the simply typed lambda-calculus with guarded recursive and coinductive types. The use of guarded recursive types ensures the productivity of well-typed programs. Guarded recursive…

Auditing is an increasingly important operation for computer programming, for example in security (e.g. to enable history-based access control) and to enable reproducibility and accountability (e.g. provenance in scientific programming).…

The Calculus of Audited Units (CAU) is a typed lambda calculus resulting from a computational interpretation of Artemov's Justification Logic under the Curry-Howard isomorphism; it extends the simply typed lambda calculus by providing…

We introduce Lineax, a library bringing linear solves and linear least-squares to the JAX+Equinox scientific computing ecosystem. Lineax uses general linear operators, and unifies linear solves and least-squares into a single,…

We present linrax, the first simplex based linear program (LP) solver compatible with the JAX ecosystem. In many control algorithms, LPs are often automatically generated and frequently solved either offline or online in the control loop.…

We present DrJAX, a JAX-based library designed to support large-scale distributed and parallel machine learning algorithms that use MapReduce-style operations. DrJAX leverages JAX's sharding mechanisms to enable native targeting of TPUs and…

We introduce fastabx, a high-performance Python library for building ABX discrimination tasks. ABX is a measure of the separation between generic categories of interest. It has been used extensively to evaluate phonetic discriminability in…

Symbolic computation, powered by modern computer algebra systems, has important applications in mathematical reasoning through exact deep computations. The efficiency of symbolic computation is largely constrained by such deep computations…

We introduce DiffOpt.jl, a Julia library to differentiate through the solution of optimization problems with respect to arbitrary parameters present in the objective and/or constraints. The library builds upon MathOptInterface, thus…

In a landscape of high-performance distributed ML systems, JAX has emerged as a framework of choice. However, JAX's modular design philosophy leaves it without a standardized checkpointing solution. In this paper, we introduce Orbax, a…

Common programming tools, like compilers, debuggers, and IDEs, crucially rely on the ability to analyse program code to reason about its behaviour and properties. There has been a great deal of work on verifying compilers and static…

QDax is an open-source library with a streamlined and modular API for Quality-Diversity (QD) optimization algorithms in Jax. The library serves as a versatile tool for optimization purposes, ranging from black-box optimization to continuous…

We develop a linear logical framework within the Hybrid system and use it to reason about the type system of a quantum lambda calculus. In particular, we consider a practical version of the calculus called Proto-Quipper, which contains the…

Dependently typed lambda calculi such as the Edinburgh Logical Framework (LF) are a popular means for encoding rule-based specifications concerning formal syntactic objects. In these frameworks, relations over terms representing formal…